Exponential Functions
Fill in the blanks: Exponential Functions are modeled using f(x) = a ∙ bx, where a is the ________ and b is the __________.
initial amount/y-intercept, constant ratio
What is the formula we use for exponential decay functions?
f(t) = a(1 - r)t
Given the exponential function formula below:
f(x) = a * bx + k
What does k represent?
A vertical translation
What is the formula we use for exponential growth functions?
f(t) = a(1 + r)t
What is the formula we use to calculate compound interest?
A = P(1 + n/r)n*t
In the exponential function below:
f(x) = 2 * 3x, what is the initial amount/y-intercept?
a = 2
In the exponential growth formula,
f(t) = a(1 - r)t, "1-r" is known as the _______.
Decay factor
Given the exponential function formula below:
f(x) = a * bx-h
What does h represent?
A horizontal translation
In the exponential growth formula,
f(t) = a(1 + r)t, "1+r" is known as the _______.
Growth factor
In the formula, A = P(1 + n/r)n*t, what does n respresent?
n = number of periods/times compounded each year
In the exponential function below:
f(x) = 4 * 1/2x, what is the constant ratio?
b = 1/2
Solve the problem:
f(t) = a(1 - r)t
a = 4500
r = 6%
t = 8 years
Round your answer to the nearest cent.
$2743.06
Given the exponential function formula below:
f(x) = a * bx
What happens to graph if a is > 1?
It gets narrower.
Solve the problem:
f(t) = a(1 + r)t
a = 4500
r = 6%
t = 8 years
Round your answer to the nearest cent.
$7,172.32
Rosa's family invested in a Certificate of Deposit (CD) for $5,000 when she was born. The interest earned is 6% and is compounded quarterly. What is the value of the CD after 18 years?
$14,605.79
What is the written form of the exponential function represented by the given table:
x y
0 4
1 12
2 36
3 108
f(x) = 4 * 3x
A video is labeled a fan favorite if it receives at least 1,000 views per day. Amelia posts a video that gets 6,465 views on the first day. The number of views decreases by 20% each day after that. In how many days total will the video stop being a fan favorite?
9 days
f(x) = 0.5x + 3
Describe the transformation.
Vertical translation 3 units up.
The population of Hillville is 10,000 residents and grows at an annual rate of 20%. What will the estimated population of Hillville be in five years?
24,883 residents
What is the difference in a 30 year loan of $80,000 between:
A: 6.45% compounded daily
B: 6.5% compounded continuously
6.5% compounded continuously: $562,295.01
6.45% compounded daily: $553,828.84
A difference of $8,466.17
Graph the exponential function given below on a piece of paper. You cannot use desmos.
f(x) = 2 * 3x
Show in desmos.
A Rolls Royce with a star roof costed Jimmy $450,000. The value of the vehicle depreciated by 12% every year. What would the value of the car be after 10 years?
Approximately $125,325
Describe the transformation given the function below:
f(x) = 3 * 4x-2 - 3
Horizontal translation 2 units to the right. Vertical translation 3 units down. Y-intercept/initial amount = 3.
The value of a pair of Fire Red 4 Jordan's increases by 10 percent every year. If the shoes were purchased 9 years ago for $140, how much is it worth today?
Approximately $330
Jennifer is saving up for a house and wants a 20% down payment. She will invest a lump sum into a savings account for 5 years that pays 4.3% annual interest and compounds monthly. After some calculations, she figures her ideal house will cost $140,000. How much should she put in the savings account today?
$22,591.84